Tayler was elected Lieutenant Governor in 1813, and re-elected in 1816, on the ticket with Daniel D. Tompkins. After Tompkins' resignation to assume the office of Vice President of the United States, Tayler served as Acting Governor from February 24 to June 30, 1817.
Article XVII of the New York State Constitution of 1777 states "...as often as the seat of government shall become vacant, a wise and descreet freeholder of this State shall be, by ballot, elected governor,..., which elections shall be always held at the times and places of choosing representatives in assembly..." This meant that, whenever a vacancy occurred, the Lt. Gov. did not succeed to the governor's office but administrated the state only until the end of the yearly term of the New York State Assembly on June 30, the successor being elected in April. This was the only occurrence of a vacancy of the governor's office under this Constitution, and in April 1817 DeWitt Clinton was elected Governor. Tayler was re-elected Lt. Gov. and re-elected in 1820.
The duel between Alexander Hamilton and Aaron Burr in 1804 is linked to comments spoken by Hamilton at Tayler's home in Albany, which were related in a letter written by Tayler's son-in-law, Dr. Charles D. Cooper, which was later published in an Albany newspaper.